${M^2}{T^2}$: The Multivariate Multistep Transition Tensor for User Mobility Pattern Prediction

Abstract

With the development of GPS technology, GPS-equipped taxicabs and users with GPS-enabled devices interact each other, and form a new mobile Internet of things (M-IoT). This paper proposes a M-IoT service framework to predict multiusers' mobility pattern by solving a cubical user-spatio-temporal probability map arising from heterogeneous sensor data. Then, the framework provides services for the traffic participants based on the prediction. To solve the stationary probability map, a novel tensor based iterative algorithm is proposed and proved to be convergent. Furthermore, the existence and uniqueness of the stationary probability is proved. The multivariate multistep transition tensor (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) model is proposed to merge massive sensor data from multisource, including time, space, and social network, so on. The eigentensor concept is proposed as the theoretical basis of the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> model. The context-aware M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> model takes into account comprehensive context factors to improve the accuracy of prediction. In the end, extensive experiments based on real GPS data are conducted to evaluate efficiency of the proposed model. The results show that the propose model has highly improved the prediction accuracy.